bel,s Functional Equation
المؤلف:
Abel, N. H.
المصدر:
Oeuvres Completes, Vol. 2 (Ed. L. Sylow and S. Lie). New York: Johnson Reprint Corp
الجزء والصفحة:
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9-8-2019
1777
bel's Functional Equation
Let 
denote the Rogers L-function defined in terms of the usual dilogarithm by
then 
satisfies the functional equation
 |
(3)
|
Abel's duplication formula follows from this identity.
REFERENCES:
Abel, N. H. Oeuvres Completes, Vol. 2 (Ed. L. Sylow and S. Lie). New York: Johnson Reprint Corp., pp. 189-192, 1988.
Bytsko, A. G. "Two-Term Dilogarithm Identities Related to Conformal Field Theory." 9 Nov 1999. http://arxiv.org/abs/math-ph/9911012.
Gordon, B. and McIntosh, R. J. "Algebraic Dilogarithm Identities." Ramanujan J. 1, 431-448, 1997.
Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, pp. 14 and 21, 1999.
Rogers, L. J. "On Function Sum Theorems Connected with the Series 
." Proc. London Math. Soc. 4, 169-189, 1907.
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